Asymptotic behaviour of a number of repeated records

Statistics and Probability Letters

Volumn 35, Issue 1, 1997, Pages 49-58

  Khmaladze, E ^a,c   Nadareishvili, M ^b   Nikabadze, A ^a  

^a A RAZMADZE MATHEMATICAL INSTITUTE   (Georgia)

^b Acad of Min of Inner Aff of G   (Georgia)

^c UNIVERSITY OF NEW SOUTH WALES   (Australia)

Author keywords

Independent random walks; Point processes; Regularly varying functions; Repetitions of record; Zipf's law

Indexed keywords

EID: 0031571386     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(96)00215-5     Document Type: Article

References (12)

1. Barbour, A.D., L. Holst and S. Janson (1992), Poisson Approximation (Clarendon Press, Oxford).
2. Brands, J., F. Steutel and R. Wilms (1994), On the number of maxima in a discrete sample, Statist. Probab. Lett. 20, 209-217.
3. Bremaud, P. (1981), Point Processes and Queues, Martingale Dynamics (Springer, New York).
4. Feller, W. (1968), An Introduction to Probability Theory and Its Application, Vol. II (Wiley, New York).
5. Hajek, J. and Z. Shidak (1967), Theory of Rank Tests (Academia, Prague).
6. Karr, A. (1991), Point Processes and Their Statistical Inference (M. Dekker, New York, 2nd ed.).
7. Khmaladze, E. and R. Chitashvili (1989), The statistical analysis of a large number of rare events and related problems, Proc. A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, Tbilisi 92, pp. 196-245.
8. Khmaladze, E. and A. Parjanadze (1986), Functional limit theorems for linear statistics from sequential ranks, Probab. Theory Related Fields 73, 585-595.
9. Mandelbrot, B. (1977), Fractals (W.H. Freeman, San Francisco).
10. Pakes, A.G. and F.W. Steutel (1995), On the number of records near the maximum. Research Report September 1995/17, Department of Statistics, The University of Western Australia, Perth, Australia (Submitted to the Australian Journal Statistics).
11. Resnick, S.I. (1987), Extreme values, regular variation and point processes, Springer Series in Applied Probability (Springer, New York).
12. Zipf, G. (1965), Human Behaviour and the Principle of Last-Effort (Addison-Wesley, Cambridge, MA).